The dynamical Casimir effect in a BEC or Parametric downconversion - - PowerPoint PPT Presentation

The dynamical Casimir effect in a BEC

• r

Parametric downconversion of phonons

• r

Cosmological particle production in the lab

Chris Westbrook Laboratoire Charles Fabry Quantum Technologies, Warsaw 12 september 2012

What to say? Electrodynamics The Casimir effect What is “dynamical”? Acoustic analogs Black holes in water

BEC

Black holes and BEC

Jaskula et al. arXiv:1207.1338

The Casimir effect An attractive force between two conducting plates:

H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51 (1948) 793.

• A. Lambrecht, “A force from nothing”, Physics World 15, 29 (2002).

Can be thought of as

• riginating from vacuum

fluctuations. (Almost) macroscopic effect containing  and c

The “Dynamical” Casimir effect Radiation of an accelerated mirror: v = v0 cos ωt real photon pairs with ω1+ ω2 = ω also looks like parametric down conversion

G.T. Moore, J. Math. Phys. 11, 2679 (1970) S.A. Fulling, P.C.W. Davies, Proc. R. Soc. London Ser. A 348, 393 (1976)

• A. Lambrecht, M.-T. Jaekel, S. Reynaud, Phys. Rev. Lett. 77, 615 (1996)

...

• P. Nation, J. Johansson, M. Bloncowe, F Nori, Rev. Mod. Phys. 84, 1 (2012)

ω1 ω2

Understanding the effect

• 1. Friction of the vacuum. An accelerated mirror

experiences a damping force when interacting with vacuum

• fluctuations. The energy is radiated as photons - in pairs

Kardar and Golestanian, Rev Mod Phys 71 1233 (1999)

• 2. Particle production accompanies any sudden

modification of the boundary conditions of a quantum field. v = v0 cos ωt ω1 ω2

• A. Lambrecht, M.-T. Jaekel, S. Reynaud,
• Phys. Rev. Lett. 77, 615 (1996)

Nphotons ∼ ωτ ⇣v c ⌘2 1 T

Toy model: single mode Parametrically driven quantum harmonic oscillator ω0 ω1 = ω0 (1 + ε) A sudden change in stiffness projects the ground state

• nto a superposition of n = 0 and n = 2 (+ higher order

even modes) → pairs (squeezed vacuum ) H ~ a0 a1†a2† + h.c.

Without motion: changing the speed of light

• 1. Change plasma frequency Yablonovitch PRL 1989
• 2. Change skin depth in a semiconductor Braggio et al EPL 2005
• 3. Use a laser induced Kerr effect Dezael, Lambrecht EPL 2010

n(t)2 = 1+ (ωp(t)/ω)2 n

Experimental observation (Wilson et al. Nature 479, 376 (2011)) 2 Josephson junctions 50 mK Drive: ω/2π =10 GHz Output analysed at ω1 = ω/2+∆ ω2 = ω/2-∆ Change in B flux changes inductance and the length of transmission line (CPW)

see also Lahteenmaki et al. arXiv:1111.5608

Sonic analog: change the speed of sound (PRL 1981) Speed of surface waves relative to flow in a water tank

• changes. Unruh suggested one could realize a sonic horizon

and observe “classical” Hawking radiation Weinfurtner et al. PRL 2011

Dynamical Casimir Gedankeneffekt in water Suddenly change the depth of the water. Look for spontaneous creation of waves (in pairs). Faraday waves ... In a BEC, c2 ~ µ/m ~ f (N, m, a, ω)

Sonic Analog to the Dynamical Casimir Effect

Carusotto, Balbinot, Fabbri, Recati, “Density correlations and analog dynamical Casimir emission of Bogoliubov phonons in a modulated atomic BEC”, EPJD 56, 391 (2010)

So, Modulate the scattering length a, in a homogenous BEC: A sudden modification of the boundary conditions for a quantum field can also lead to the spontaneous emission of correlated pairs ...

The team (... is looking for a post doc)

Guthrie Partridge Marie Bonneau Jean-Christophe Jaskula Denis Boiron C I W Josselin Ruadel Rafael Lopes

Apparatus

laser trap BEC particle detector Detect atoms in excited cloud of He* in momentum space. Time of flight 307 ms He*: the 23S1 state 20 eV modulate trap laser intensity

“Time of flight” observation

typically 105 atoms time of flight ~ 300 ms width of TOF ~ 10 ms We record x,y,t for every detected atom. Get velocity distribution and correlation function.

trap detector

46 cm

quasi-condensate

ωρ = 1.5 kHz, ωz = 7 Hz lz ~ 1 mm µ ~ 3 kHz

Analog to the dynamical Casimir effect

Generate excitations: ωk = ωmod/2 as should be the case for a parametric

• scillator

H ~ bk† b-k†+ h.c.

modulation: Δt = 30 ms Δν = 0.1 νtrap ωmod/2π = 0.5 - 5 kHz

inspired by Carusotto et al EPJD 2010

sinusoidal modulation (velocity scale)

n(v)

Correlation function pair histogram of single shots histogram of different shots

g(2)(v,v′) = g(2)(v,v′=-v) n(v)

what is the energy

• f this excitation?

v=k/m

(ω2 − ω1) = ω = 1 2m ⇤ p2(p2 + 4m2c2) (ω2 − ω1) = ω = ⌅ 2k2 2m 2k2 2m + 2mc2 ⇥

How to show ωmod = ωk + ω-k ωmod = 2ωk = α

fit: α = 2.2

c = 8 mm/s

¡Modulation ¡frequency ¡(Hz)

a

1000

b

2000 3000 4000 5000 Vertical ¡velocity ¡ ¡ ¡ ¡ ¡ ¡(cm/s)

vz 2.0 1.5 1.0 0.5 0.0

1000 2000 3000 4000 5000 ¡Modulation ¡frequency ¡(Hz)

5 10 15 mm/s vertical velocity

from correlation function from density we can verify α = 2 using Bragg scattering

Sudden compression of a BEC Increase trap laser intensity by factor of 2 in ~ 30 µs (Δω = 5 kHz) hold ~ 30 ms

Laser intensity t (µs) (quasi-)condensate parameters: lz = 0.5 mm ωρ = 1.5 kHz, ωz = 7 Hz Highly elongated µ ~ 3 kHz c ~ 1 cm/s ξ = 500 nm

• 100
• 50

Distribution along z

Correlations in the v - v′ plane HBT effect v,-v correlation

1.08 1.06 1.04 1.02 1.00 0.98 0.96 3 2 1

• 1
• 2
• 3

δv

• 2
• 4
• 6
• 6
• 4
• 2

pair histogram of single shots histogram of different shots

g(2)(v,v′) =

v cm/s v′ cm/s

v-v′ (cm/s) v = v′ axis

(projection)

Related observations

“Faraday waves ...” Engels et al. PRL 98 095301 (2007) In a mag. trap, modulate transverse confinement, in situ images. Spatial period corresponds to ω/2 “Twin atom beams” Bücker et al.

• Nat. Phys. 7, 608 (2011)

Modulate trap centre to excite transverse mode collisions produce longitudinally moving atoms. Subpoissonian difference ∆ N2 ~ 0.37 (or 0.11)

More related observations

“Cosmology to cold atoms:

• bservation of Sakharov
• scillations ...”

Hung, Gurarie and Chin arXiv:.1209.0011 Suddenly change the scattering length; in situ images show expanding and propagating density fluctuations. Recalls theoretical proposals by Fedichev and Fischer PRA 2004 Jain, Weinfurtner, Visser and Gardiner, PRA 2007

So far so good, but... Nonzero temperature: kBT/h = 4 kHz (200 nK) thermally stimulated Lack of sub-Poissonian statistics: ∆ (N1-N2)2 / (N1+N2) > 1 A sub-Poissonian variance would demonstrate that the result cannot be due to fluctuations of classical waves. N2 N1 Due to T ≠ 0 ?

v2

Variance

No violation of Cauchy-Schwarz inequality (see P . Deuar)

Sonic Hawking radiation in BEC

Garay, Anglin, Cirac, Zoller, PRA 63, 023611 (2001), “Sonic black holes in dilute BECs” Balbinot et al PRA 78 021603 (2008), “Nonlocal density correlations as a signature of Hawking radiation from acoustic black holes” Lahav et al. PRL 105, 240401 (2010), “Realization of a sonic black hole analog in a BEC”.

A black hole produces correlated particles is very appealing to quantum opticians - looks like a parametric oscillator

H ~ a0 a1†a 2† + h.c.

Experimental realization of a horizon

x V(x)

Moving shadow Laser BEC v ~ 1 cm/s d ~ 1mm t ~ 100 ms

Signature of Hawking radiation in p-space

P .-E. Larré, N. Pavloff

Correlations in momentum space

• 2
• 4
• 6
• 6
• 4
• 2

v cm/s v′ cm/s Amplitude of correlations?

Conclusions and outlook

• Trap modulation certainly produces correlated excitations
• beying ωmod = ωk + ω-k
• Here kT/h ~ 4 kHz. Excitations not from vacuum.
• No sub-Poissonian number difference (yet)
• Simulation of particle production the expansion of the early

universe? (Jain, Weinfurtner, Visser, Gardiner, PRA 2007, Fedichev, Fischer PRA 2004)

• Other aspects of quantum transport?

Tianks